My reading of the paper was that it was a complete basis for the three particle system (modulo the center of mass) subject to the antisymmetry condition on the three electrons, which was originally $\begin{eqnarray} \Psi(z_1,z_2,z_3) &=&-\Psi(z_2,z_1,z_3) = \\
\Psi(z_2,z_3,z_1) &=&-\Psi(z_1,z_3,z_2) = \\
\Psi(z_3,z_1,z_2) ...

Short answer: Yes
Slightly longer answer:
If you scatter the wavefunction of a propagating electron from a potential (surface of a material for example), it generally splits into two parts - a transmitted part and a reflected part.
As the names indicate, the reflected part represents a 'reflected' electron, the transmitted part a transmitted one.
However, ...

The atom has some charge distribution $\rho(r)$. We don't don't know what form the function $\rho(r)$ has, but we do know it depends only on $r$ because an atom is spherically symmetric.
When you have a spherical charge distribution the potential at a distance $r$ is simply due to the total charge inside the distance $r$:
$$ V(r) = ...

Why are electrons alike but photons not?
Because it takes a given amount of an energy to make an electron: 511keV. That's the energy of an electron at rest. A fast-moving electron comprises more energy than an electron just sitting there in front of you, but if you were to stop it by removing the kinetic energy, its rest-energy is 511keV, and its mass ...

It's a good question, and one that puzzled me for a while as well. However the answer is very simple.
For a massive particle like an electron the total energy is given by:
$$ E^2 = p^2c^2 + m^2 c^4 $$
where $p$ is the momentum and $m$ is the rest mass of the electron. Electrons can obviously have any momentum you want, so the total energy can be any value ...

Electron and holes are Fermions (particles with spin 1/2). This means that no two particles can share the same microstate. The Fermi-Dirac distribution describes how Fermions fill the available states consistent with this property.
Bosons on the other hand (particles with integer spin) can occupy the same state. The Bose-Einstein distribution describes how ...

this is a description of an interaction between the electron and photons, which would collapse the wavefunction (right?).
No this isn't right. As long as the system stays isolated, the interaction simply means that there are cross terms in the relevant Hamiltonian and that you have a two-particle quantum system, whose state space is the tensor product ...

Let's look at where the electromagnetic interaction comes from in hydrogen.
At first quantization you have a multiparticle system so the wavefunction is defined as $\psi=\psi(x_1,y_1,z_1,x_2,y_2,z_2,t)$ and the point is to write the Hamiltonian.
And the Hamiltonian comes from the Lagrangian. For a single particle of charge $q$ in an external ...

The discreteness of the allowed orbitals is a consequence of quantum mechanics, which was conceived precisely to explain this observation, among other things. However, the orbitals are not orbits - there is no "motion" in the classical sense going on, and an electron in an orbital does not have a fixed distance to the nucleus (it may even have non-zero ...

Electron as a standing wave
Yes, the electron is a standing wave. See atomic orbitals on Wikipedia: "The electrons do not orbit the nucleus in the sense of a planet orbiting the sun, but instead exist as standing waves".
I couldn't understand how come Bohr who interpreted electron as a particle, formulated an equation for electron's angular ...

I now come to my point, why one restricts a particle's motion to some discrete set of distances? Is it to provide a theory on the particle's stability?
An attempt at an answer to your first question anyway.
The electrons surrounding an atom need to obey energy level (and other) rules. As you mention distance, if you imagine that the further away the ...

As pointed in the comment by @CuriousOne, there is indeed a paper providing such explanation ("The photoelectric effect without photons" by Lamb and Scully).
It was however later found to be faulty. A very good review and references on this can be found in these answers to a different question posted on this website, but apparently there is no consensus on ...

This is because usually a electron can ONLY stay in certain energy states in a given atom, this is because of the quantum mechanical forces such as strong force, and Heisenberg uncertainty principles.
Let me explain further, as electron gets closer to an atom the electrostatic & other quantum mechanical forces between the electron starts pulling it, and ...

However it did pass within Δx of the electron.
The Δx is not the difference in space with the electron, as the electron is bound to a nucleus with a potential simulated by "an infinite potential well" . The Δx is related to the whole system, from the center of its mass as a possible location to start with.
So the problem is : "photon + atom" as a ...

The electrons do not even enter the wire, because the redox reaction between the substances in each of the nodes never occurs. Once the wire is connected to each of the nodes, electricity will flow through as electrons will be more attracted to the node with the greater reduction potential.

The battery does create an electric field near itself that forces electrons away from it. As they travel they begin to build up on the bends of the wire. This is known as feedback. The next electrons coming by are repelled away from this build up allowing them to travel around instead of just directly away from the battery. This is how electrons can travel ...

Lets run a few numbers. Go with electrons. 200keV electrons (like from a standard transmission electron microscope). These have a velocity of just about 2E8 m/sec (yes, relativistic effects need to be taken into account). One nano-ampere is a little more than 6E9 electrons per second. Dividing through, that gives you, on average, 30 electrons per meter of ...

Start by considering a long pipe with water flowing through it. We'll assume the rate of flow is slow, so the current of water is small. This means water entering the pipe at one end will take a long time to flow all the way along the pipe to the other end.
However suppose we generate a pressure wave at one end of the pipe. A pressure wave in water is just ...

If you have $N$ point particles in a volume $V$, i.e. the particle density is $n=N/V$. Then any particle has a volume $\frac{V}{N}=\frac{1}{n}$ for itself. Imagine dividing $V$ in $N$ little cubes and all cubes hold one particle, than the distance between a particle and its nearest neighbour is $\left(\frac{V}{N}\right)^{1/3}=\frac{1}{n^{\frac{1}{3}}}$, ...

It's not a stupid question. In fact, Quantum Field Theory is the field of physics that seeks to answer exactly this question. In QFT, in addition to the electromagnetic field, there is a single electron field that extends throughout the universe. Stable ripples in the electron field constitute individual electrons. Every fundamental particle has a ...

From the famous Double-slit experiment, it is clear that electrons do behave as wave as well as particle. When it is detected by geiger counter, "click" sound appears & no matter how greatly the voltage is decreased along the cathode tube, "click" & never "half click" appears. So, electrons always arrive at lumps like bullets. However, unlike bullets ...

The electromagnetic wave is a classical theory while matter waves are quantum mechanical. The wave aspect is a mathematical abstraction which allows us to predict future quantum states of the electron with a known probability.

Is it possible to decrease the mass of the object?
Perhaps surprisingly the answer is yes. All you need to do is it drop it. Then some of the object's mass-energy, which we call potential energy, is converted into kinetic energy, which ends up getting dissipated. You're then left with a mass deficit. The mass of the object is reduced.
It is known ...

Why don't electrons collapse into black holes?
Because the electron isn't a point-particle. Its field is what it is. It isn't some speck that has a field, it is that field. There's energy in that field, that energy has a mass-equivalence, and it doesn't have a zero volume. Also note that we can diffract electrons. And that the Einstein-de Haas effect ...

The angular momentum and charge of an electron are both large enough that a black hole would not form. If you believe classical general relativity all the way down to the scale of an electron (and you really shouldn't), then the electron will form a naked singularity.
More exactly, for the case of a spinning body, the horizon is at the zero of
$$r^{2} - ...

Electrons accelerating due to EM fields in the presence of gravity field radiate - examples are cyclotron radiation, antenna emissions.
In the absence of EM field, whether the electrons radiate in the presence of gravitational field is theoretically problematic question, because Earth is not an inertial system, so Maxwell's equations should not apply ...

Let us not ignore the fact that there will be some overlaps too. For example, when there's a jump from 10 to 22 and a jump from 11 to 55, the spectral lines will overlap because 1/(10*10)-1/(22*22)=1/(11*11)-1/(55*55). Hence the actual number of spectral lines will be less than or equal to n*(n-1)*(1/2).

How to explain what an electron is to someone new to physics?
I think you can come up with an easy-reading explanation that's physically correct. There's plenty of clues in the literature if you're willing to play detective. For example see pair production. We quite literally make an electron (and a positron) out of light. And then when we annihilate ...

Here is a more complicated answer:
I am going to try my best, ok?
An electron is a negative elementary charge subatomic particle of an atom. It was once known as a beta particle, but it is now an electron. It takes electromagnetic, gravity, and weak interactions into play. In Coulombs, it's charge is approximately $-1.6 * 10^{-19} C$ and it's mass in ...

Electron is a particle with mass and a certain probability of being found at a given distance around the nucleus of an atom at a certain time. It caries a negative charge which makes chemical reactions possible since chemical reactions are driven by the electrostatic forces between electrons and positively charged protons which reside in the nucleus of the ...

Hmmm... I'll take a crack at it.
An electron is a negatively charged subatomic particle that orbits the nucleus of an atom, which contains a positively charged subatomic particle called a proton and a neutral subatomic particle called a neutron.

I don't think it's quite that simple. The resistivity may be related to the barrier potential energy separating the two reservoirs, which directly modulates tunneling in the obvious way (higher energy = less tunneling). But there is one barrier which classically you'd describe with an infinite resistance (a Dirac $\delta$-function potential) which admits ...

In quantum mechanics, things are not "particles" or "waves" - they may behave like both, or like neither. But a quantum object "is" neither of those - it is a quantum state, usually described as a vector in a Hilbert space.
The Bohr model of the electron orbiting the atom is false (for one inconsistency, that of moving charges classically radiating, see ...

Who says electrons are not waves in the atom?
Discard your bygone, quaint, outdated, perplexing, stupifying, nonsense idea that electrons move in a solar-system sort of orbits. That model(attributed to Rutherford) was an attempt to understand the atomic arena of Nature; unfortunately it was far from being correct as it had many in-built flaws.
Then the ...

I think the default that electron is a particle is taught us first because of historical reason. You have to understand the newtonian universe before the quantum mechanics; else it would be too complicated.
The atomic model was first made with electron on discrete observable routes. The next step was the thinking that they have to be stable and quantized so ...

A degenerate gas is one where more than one electron (in fact, two) occupies each possible low-energy state up to the Fermi energy. I suppose the term "degenerate" comes from the multiple occupancy of each energy level.

A normal gas consists of particles that do not interact much except for elastic collisions.
Often, describing a gas in a simplified way ignoring the other interactions completely is good enough.
This simplified model is the "ideal gas".
This simplified description fits for the electron gas also, as long as the pauli exclusion principle does not become ...

Something analogous to the Fermi-Dirac distribution function will probably work pretty well for the electrons in the Sun; see for example this PDF. You may need to put in some "fudge factors" for their interaction energy with the rest of the proton soup, but you're in some luck, because the interaction energy in the Sun is actually mostly lower than the ...